STRUCTURAL TRANSITIONS AND SHEAR STABILITY OF POLYATOMIC LAYERS

摘要

A two-dimensional model is presented for a crystalline layer of nonlinearly interacting atoms confined between rigid boundaries and subjected to shear. The deformation energy is shown to consist of periodic and gradient terms . The equilibrium equation in the sine-Helmholtz form , with two characteristic coherence lengths, is exactly solved to obtain relations between cell dimensions (large superstructure periods) and the amplitude of the displacement field, which specify conditions for the bifurcation of solutions. The results indicate a transition from a trivial solution ,representing a low-gradient displacement field, to a solution describing a high-gradient microscopic field. The latter remains stable up to a certain amplitude and then passes into an excited,but also stable state.